Post by Cynicus Rex on Oct 18, 2018 15:08:12 GMT
Source: github.com/ystael/chicago-ug-math-bib (which I found on Reddit)
What follows are only the books mentioned, so make sure to also read the additional remarks on the former web page before reading or buying.
Elementary math
Algebra
Geometry
Foundations
Problemsolving
Calculus
Intermediate math
Foundations
Abstract algebra
Linear algebra
Number theory
Combinatorics, discrete math
Multivariable calculus
Differential equations
Real analysis
Complex analysis
Point set topology
Geometry
Differential geometry
Advanced math
Foundations
Problem solving
Abstract algebra
Group theory
Ring theory
Commutative algebra, Homological algebra
Number theory
Combinatorics, discrete math
Measure theory
Probability
Functional analysis
Complex analysis
Harmonic analysis
Differential equations
Differential topology
Algebraic topology
Differential geometry
Geometric measure theory
Algebraic geometry
This is an annotated bibliography of books that may be useful to undergraduates in pure mathematics. I wrote the original version, with the help of some classmates, during my final year (1997-98) at the University of Chicago. To my great surprise, it has been useful to many people over the intervening years, and I am now maintaining it and accepting contributions on Github.
Elementary math
Algebra
- Gelfand - Algebra: www.goodreads.com/book/show/2140100.Algebra
- Gelfand, Glagoleva, Shnol - Functions and graphs: www.goodreads.com/book/show/946674.Functions_and_Graphs
- Gelfand, Glagoleva, Kirillov - The method of coordinates: www.goodreads.com/book/show/4603880-the-method-of-coordinates
Geometry
- Euclid - The elements: www.goodreads.com/book/show/214441.Euclid_s_Elements
- Coxeter - Geometry revisted: www.goodreads.com/book/show/207954.Geometry_Revisited
Foundations
- Rucker - Infinity and the mind: www.goodreads.com/book/show/274050.Infinity_and_the_Mind
Problemsolving
- Larson - Problem solving through problems: www.goodreads.com/book/show/2146185.Problem_Solving_Through_Problem
- Pólya - How to solve it: www.goodreads.com/book/show/192221.How_to_Solve_It
- Pólya - mathematics and plausible reasoning, I and II: www.goodreads.com/book/show/19943982-mathematics-and-plausible-reasoning-v1-2
Calculus
- Spivak - Calculus: www.goodreads.com/book/show/4426208-calculus
- Spivak - The hitchhiker's guide to calculus: www.goodreads.com/book/show/862643.The_Hitchhiker_s_Guide_to_Calculus
- Hardy - A course of pure mathematics: www.goodreads.com/book/show/573330.A_Course_of_Pure_Mathematics
- Courant - Differential and integral calculus: www.goodreads.com/book/show/2298338.Differential_And_Integral_Calculus
- Apostol - Calculus:
www.goodreads.com/book/show/282035.Calculus_Volume_1,
www.goodreads.com/book/show/53798.Calculus_Volume_2
Intermediate math
Foundations
- Halmos - Naive set theory: www.goodreads.com/book/show/558194.Naive_Set_Theory
- Fraenkel - Abstract set theory: www.goodreads.com/book/show/3146579-abstract-set-theory
- Kunen - Set theory: An introduction to independence results: www.goodreads.com/book/show/558199.Set_Theory
- Ebbinghaus, Flum, Thomas - Mathematical logic: www.goodreads.com/book/show/1768355.Mathematical_Logic
- Enderton - A mathematical introduction to logic: www.goodreads.com/book/show/250872.A_Mathematical_Introduction_to_Logic
- Chang, Keisler - Model theory: www.goodreads.com/book/show/20128440-model-theory
- Landau - Foundations of analysis: www.goodreads.com/book/show/53742.Foundations_of_Analysis
Abstract algebra
- Dummit, Foote - Abstract algebra: www.goodreads.com/book/show/264543.Abstract_Algebra
- Herstein - Topics in algebra: www.goodreads.com/book/show/1264762.Topics_in_Algebra
- Artin - Algebra: www.goodreads.com/book/show/20063154-algebra
- Jacobson - Basic algebra I: www.goodreads.com/book/show/7812046-basic-algebra-i
- Hungerford - Algebra: www.goodreads.com/book/show/264515.Algebra_Graduate_Texts_in_Mathematics_
- Lang - Algebra: www.goodreads.com/book/show/79780.Algebra
- Mac Lane, Birkhoff - Algebra: www.goodreads.com/book/show/534605.Algebra
Linear algebra
- Halmos - Finite dimensional vector spaces: www.goodreads.com/book/show/692030.Finite_Dimensional_Vector_Spaces
- Curtis - Abstract linear algebra: www.goodreads.com/book/show/3222801-abstract-linear-algebra
- Greub - Linear algebra: www.goodreads.com/book/show/3703166-linear-algebra
- Greub - Multilinear algebra: www.goodreads.com/book/show/4548514-multilinear-algebra
Number theory
- Ireland, Rosen - A classical introduction to modern number theory: www.goodreads.com/book/show/585557.A_Classical_Introduction_to_Modern_Number_Theory_Graduate_Texts_in_Mathematics_
- Burn - A pathway into number theory: www.goodreads.com/book/show/1977970.A_Pathway_Into_Number_Theory
- Hardy, Wright - An introduction to the theory of numbers theory: www.goodreads.com/book/show/585623.An_Introduction_to_the_Theory_of_Numbers
- Chandrasekharan - Introduction to analytic number theory: www.goodreads.com/book/show/15911641-introduction-to-analytic-number-theory
- Apostol - Introduction to analytic number theory: www.goodreads.com/book/show/241408.Introduction_to_Analytic_Number_Theory
Combinatorics, discrete math
- Graham, Knuth, Patashnik - Concrete mathematics: www.goodreads.com/book/show/112243.Concrete_Mathematics
Multivariable calculus
- Spivak - Calculus on manifolds: www.goodreads.com/book/show/328647.Calculus_On_Manifolds
- Do Carmo - Differential forms and applications: www.goodreads.com/book/show/233053.Differential_Forms_and_Applications
Differential equations
- Arnold - Ordinary differential equations: www.goodreads.com/book/show/1115400.Ordinary_Differential_Equations
- Hurewicz - Lectures on ordinary differential equations: www.goodreads.com/book/show/3637626-lectures-on-ordinary-differential-equations
Real analysis
- Rudin - Principles of mathematical analysis: www.goodreads.com/book/show/292079.Principles_of_Mathematical_Analysis
- Apostol - Mathematical analysis: www.goodreads.com/book/show/53800.Mathematical_Analysis
- Gelbaum, Olmsted - Counterexamples in analysis: www.goodreads.com/book/show/818070.Counterexamples_in_Analysis
- Kolmogorov, Fomin - Introductory real analysis: www.goodreads.com/book/show/218517.Introductory_Real_Analysis
- Haaser, Sullivan - Real analysis: www.goodreads.com/book/show/3459109-real-analysis
- Hewitt, Stromberg - Real and abstract analysis: www.goodreads.com/book/show/3992197-real-and-abstract-analysis
- Dieudonné - Foundations of modern analysis: www.goodreads.com/book/show/6520344-foundations-of-modern-analysis
- Rudin - Real and complex analysis: www.goodreads.com/book/show/1039015.Real_and_Complex_Analysis
- Lang - Real and functional analysis: www.goodreads.com/book/show/3395988-real-and-functional-analysis-graduate-texts-in-mathematics
- Royden - Real analysis: www.goodreads.com/book/show/218522.Real_Analysis
Complex analysis
- Ahlfors - Complex analysis: www.goodreads.com/book/show/2437190.Complex_Analysis
- Conway - Functions of one complex variable I: www.goodreads.com/book/show/19318638-functions-of-one-complex-variable-i
- Narasimhan - Complex analysis in one variable: www.goodreads.com/book/show/18565987-complex-analysis-in-one-variable
- Rudin, Real and complex analysis: www.goodreads.com/book/show/1039015.Real_and_Complex_Analysis
- Palka - An introduction to complex function theory: www.goodreads.com/book/show/1825029.An_Introduction_to_Complex_Function_Theory
Point set topology
- Munkres - Topology: a first course: www.goodreads.com/book/show/1894071.Topology
- Willard - General topology: www.goodreads.com/book/show/116423.General_Topology
- Kelley - General topology: www.goodreads.com/book/show/2118994.General_Topology
- Steen, Seebach - Counterexamples in topology: www.goodreads.com/book/show/116419.Counterexamples_in_Topology
- Dugundji - Topology: www.goodreads.com/book/show/1503831.Topology
- Armstrong - Basic Topology: www.goodreads.com/book/show/10149070-basic-topology
- Simmons - Introduction to Topology and Modern Analysis: www.goodreads.com/book/show/208761.Intro_Topology_Modern_Analysis
Geometry
- Coxeter - Introduction to geometry: www.goodreads.com/book/show/207951.Introduction_to_Geometry
- Hilbert - Foundations of geometry: www.goodreads.com/book/show/1635912.The_Foundations_of_Geometry
- Hartshorne - Geometry: Euclid and beyond: www.goodreads.com/book/show/214443.Geometry
Differential geometry
- Guillemin, Pollack - Differential topology: www.goodreads.com/book/show/1246834.Differential_Topology
- Do Carmo, Differential geometry of curves and surfaces: www.goodreads.com/book/show/211190.Differential_Geometry_of_Curves_and_Surfaces
- Spivak - A comprehensive introduction to differential geometry, 1 and 2:
www.goodreads.com/book/show/211192.A_Comprehensive_Introduction_to_Differential_Geometry_Vol_1,
www.goodreads.com/book/show/410814.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_2?ac=1&from_search=true
Advanced math
Foundations
- Mac Lane - Categories for the working mathematician: www.goodreads.com/book/show/1088482.Categories_for_the_Working_Mathematician
- Jech - Set Theory: www.goodreads.com/book/show/558195.Set_Theory
- Foreman, Kanamori, et al - Handbook of Set Theory: www.goodreads.com/book/show/6698683-handbook-of-set-theory-3-volume-set
Problem solving
- Pólya, Szegö - Problems and theorems in analysis I and II:
www.goodreads.com/book/show/1894050.Problems_and_Theorems_in_Analysis_I,
www.goodreads.com/book/show/1874241.Problems_and_Theorems_in_Analysis_II
Abstract algebra
- Jacobson - Basic algebra II: www.goodreads.com/book/show/20681530-basic-algebra-ii
Group theory
- Alperin, Bell - Groups and representations: www.goodreads.com/book/show/2855410-groups-and-representations
- Rotman - Introduction to the theory of groups: www.goodreads.com/book/show/558480.An_Introduction_to_the_Theory_of_Groups
- Gorenstein - Finite groups: www.goodreads.com/book/show/11495195-finite-groups
- Humphreys - Introduction to Lie algebras and representation theory: www.goodreads.com/book/show/1825026.Introduction_to_Lie_Algebras_and_Representation_Theory
- Fulton, Harris - Representation theory: a first course: www.goodreads.com/book/show/585309.Representation_Theory
Ring theory
- Kaplansky - Fields and rings: www.goodreads.com/book/show/2604440-fields-and-rings
- Anderson, Fuller - Rings and categories of modules: www.goodreads.com/book/show/2074932.Rings_and_Categories_of_Modules
- Morandi - Field and Galois theory: www.goodreads.com/book/show/241206.Field_and_Galois_Theory
- Lam - A first course in noncommutative rings: www.goodreads.com/book/show/5736258-a-first-course-in-noncommutative-rings
- Atiyah, Macdonald - Introduction to commutative algebra: www.goodreads.com/book/show/1549790.Introduction_To_Commutative_Algebra
- Matsumura - Commutative ring theory: www.goodreads.com/book/show/2304602.Commutative_Ring_Theory
- Eisenbud - Commutative algebra with a view toward algebraic geometry: www.goodreads.com/book/show/1969546.Commutative_Algebra
- Kaplansky - Commutative rings: www.goodreads.com/book/show/3423833-commutative-rings
- Weibel - An introduction to homological algebra: www.goodreads.com/book/show/1331929.An_Introduction_to_Homological_Algebra
Number theory
- Weil - Basic number theory: www.goodreads.com/book/show/587109.Basic_Number_Theory
- Narkiewicz - Introduction to the elementary and analytic theory of algebraic numbers: www.goodreads.com/book/show/1788180.Elementary_and_Analytic_Theory_of_Algebraic_Numbers
- Silverman - The arithmetic of elliptic curves: www.goodreads.com/book/show/174316.The_Arithmetic_of_Elliptic_Curves
- Koblitz - p-adic numbers, p-adic analysis, and zeta functions: www.goodreads.com/book/show/753815.p_adic_Numbers_p_adic_Analysis_and_Zeta_Functions_Graduate_Texts_in_Mathematics_
- Fröhlich, Taylor - Algebraic number theory: www.goodreads.com/book/show/3460031-algebraic-number-theory
- Lovasz - Combinatorial problems and exercises: www.goodreads.com/book/show/2382199.Combinatorial_Problems_and_Exercises_AMS_Chelsea_Publishing_
- Stanley - Enumerative combinatorics I: www.goodreads.com/book/show/18791495-enumerative-combinatorics
- Bollobás - Modern graph theory: www.goodreads.com/book/show/388048.Modern_Graph_Theory
Measure theory
- Halmos - Measure theory: www.goodreads.com/book/show/743983.Measure_Theory
- Federer - Geometric measure theory: www.goodreads.com/book/show/2278402.Geometric_Measure_Theory
Probability
- Feller - Introduction to probability theory and its applications:
www.goodreads.com/book/show/2378167.An_Introduction_to_Probability_Theory_and_Its_Applications_Volume_1
www.goodreads.com/book/show/746145.An_Introduction_to_Probability_Theory_and_Its_Applications_Volume_II
Functional analysis
- Conway - A course in functional analysis: www.goodreads.com/book/show/1472955.A_Course_in_Functional_Analysis
- Dunford, Schwartz - Linear operators:
www.goodreads.com/book/show/2195562.Linear_Operators_Part_1,
www.goodreads.com/book/show/2195563.Linear_Operators_Part_2,
www.goodreads.com/book/show/2195561.Linear_Operators_Part_3 - Kadison, Ringrose - Fundamentals of the theory of operator algebras:
www.goodreads.com/book/show/1710331.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_I,
www.goodreads.com/book/show/1710329.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_II,
www.goodreads.com/book/show/8179519-fundamentals-of-the-theory-of-operator-algebras-volume-iii,
www.goodreads.com/book/show/1710336.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_IV - Kreyszig - Introductory functional analysis with applications: www.goodreads.com/book/show/241452.Introductory_Functional_Analysis_with_Applications
- Zimmer - Essential Results of Functional Analysis: www.goodreads.com/book/show/5440626-essential-results-of-functional-analysis
Complex analysis
- Andersson - Topics in complex analysis: www.goodreads.com/book/show/3516869-topics-in-complex-analysis
- Gunning, Rossi - Analytic functions of several variables: www.goodreads.com/book/show/7147564-analytic-functions-of-several-complex-variables
- Whitney - Complex analytic varieties: www.goodreads.com/book/show/31297342-complex-analytic-varieties
- Narasimhan - Compact Riemann surfaces: www.goodreads.com/book/show/3913058-compact-riemann-surfaces
- Jost - Compact Riemann surfaces: www.goodreads.com/book/show/2581888-compact-riemann-surfaces
- Weyl - The concept of a Riemann surface: www.goodreads.com/book/show/6206794-the-concept-of-a-riemann-surface
Harmonic analysis
- Katznelson - An introduction to harmonic analysis: www.goodreads.com/book/show/600474.An_Introduction_to_Harmonic_Analysis
- Rudin - Fourier analysis on groups: www.goodreads.com/book/show/148572.Fourier_Analysis_on_Groups
- Hewitt, Ross - Abstract harmonic analysis: www.goodreads.com/book/show/5852764-abstract-harmonic-analysis
- Stein, Weiss - Introduction to Fourier analysis on Euclidean spaces: www.goodreads.com/book/show/30082488-introduction-to-fourier-analysis-on-euclidean-spaces-pms-32-volume-32
- Helgason - Groups and geometric analysis: www.goodreads.com/book/show/4481022-groups-and-geometric-analysis-integral-geometry-invariant-differential
Differential equations
- Taylor - Partial differential equations I: basic theory: www.goodreads.com/book/show/6715867-partial-differential-equations-i
- Evans, Partial differential equations: www.goodreads.com/book/show/7993898-partial-differential-equations
- Hörmander - The analysis of linear partial differential operators I: www.goodreads.com/book/show/2720260-the-analysis-of-linear-partial-differential-operators-i
- Olver - Equivalence, invariants and symmetry: www.goodreads.com/book/show/3353230-equivalence-invariants-and-symmetry
Differential topology
- Hirsch - Differential topology: www.goodreads.com/book/show/1688091.Differential_Topology
- Lang - Differential and Riemannian manifolds: www.goodreads.com/book/show/737509.Differential_and_Riemannian_Manifolds
- Warner - Foundations of differentiable manifolds and Lie groups: www.goodreads.com/book/show/12428059-foundations-of-differentiable-manifolds-and-lie-groups
Algebraic topology
- Massey - A basic course in algebraic topology: www.goodreads.com/book/show/116424.A_Basic_Course_in_Algebraic_Topology
- Fulton - Algebraic topology: a first course: www.goodreads.com/book/show/1076691.Algebraic_Topology
- Bott, Tu - Differential forms in algebraic topology: www.goodreads.com/book/show/1246831.Differential_Forms_in_Algebraic_Topology
- Spanier - Algebraic topology: www.goodreads.com/book/show/4113534-algebraic-topology
- Rotman - An introduction to algebraic topology: www.goodreads.com/book/show/2324277.An_Introduction_to_Algebraic_Topology
- Stillwell - Classical topology and combinatorial group theory: www.goodreads.com/book/show/1669283.Classical_Topology_and_Combinatorial_Group_Theory
- Bredon - Topology and geometry: www.goodreads.com/book/show/1748333.Topology_and_Geometry
Differential geometry
- Spivak - A comprehensive introduction to differential geometry, 3-5:
www.goodreads.com/book/show/2252071.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_3,
www.goodreads.com/book/show/676934.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_4,
www.goodreads.com/book/show/643246.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_5 - Helgason - Differential geometry, Lie groups, and symmetric spaces: www.goodreads.com/book/show/1585857.Differential_Geometry_Lie_Groups_and_Symmetric_Spaces
- Kobayashi, Nomizu - Foundations of differential geometry:
www.goodreads.com/book/show/211193.Foundations_of_Differential_Geometry_Volume_1,
www.goodreads.com/book/show/6984384-foundations-of-differential-geometry-volume-2 - Rosenberg - The Laplacian on a Riemannian manifold: www.goodreads.com/book/show/2324280.The_Laplacian_on_a_Riemannian_Manifold
- Do Carmo - Riemannian geometry: www.goodreads.com/book/show/233052.Riemannian_Geometry
- Boothby - Introduction to differentiable manifolds and Riemannian geometry: www.goodreads.com/book/show/683585.An_Introduction_to_Differentiable_Manifolds_and_Riemannian_Geometry_Revised
Geometric measure theory
- Morgan - Geometric measure theory: a beginner's guide: www.goodreads.com/book/show/6455214-geometric-measure-theory
- Mattila - Geometry of sets and measures on Euclidean spaces: www.goodreads.com/book/show/558168.Geometry_of_Sets_and_Measures_in_Euclidean_Spaces
- Federer - Geometric measure theory: www.goodreads.com/book/show/2278402.Geometric_Measure_Theory
- Falconer - The geometry of fractal sets: www.goodreads.com/book/show/558112.The_Geometry_of_Fractal_Sets
Algebraic geometry
- Harris - Algebraic geometry: a first course: www.goodreads.com/book/show/1861684.Algebraic_Geometry
- Shafarevich - Basic algebraic geometry 1: www.goodreads.com/book/show/1642686.Basic_Algebraic_Geometry_Volume_1
- Mumford - Algebraic geometry I: complex projective varieties: www.goodreads.com/book/show/2017827.Algebraic_Geometry_I
- Griffiths, Harris - Principles of algebraic geometry: www.goodreads.com/book/show/1690529.Principles_of_Algebraic_Geometry
- Hartshorne - Algebraic geometry: www.goodreads.com/book/show/338302.Algebraic_Geometry